##  [Non-Rectifiable Boundary](/non-rectifiable-boundary) 

  ##  [Non-Rectifiable Boundary](https://puremath.quantumdictionary.io/non-rectifiable-boundary-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A boundary for which classical rectifiability fails: in the planar case it has no finite arclength representation as a countable union of Lipschitz images, typically because oscillation at small scales produces infinite length or prevents well-defined tangent a.e.